- Basic concepts and calculation techniques: set theory, real and complex numbers (in particular: Cartesian coordinates and polar coordinates, roots of complex numbers), solving equations and inequalities;
- Functions of one variable: basic concepts and elementary functions, continuity, symmetry, monotony, inverse function, rational functions, asymptotes, sequences and series (limit value concept, calculation rules), power series (convergence behavior and calculation with power series), exponential function and logarithm, trigonometric functions;
- Differentiation (one-dimensional): definition of limit values and significance of derivation, computational techniques, implicit derivation, mean value theorem, extreme values, de l'Hospital rule, Taylor expansion, representation of functions by Taylor series, applications (error estimation and approximation);
- Integration (one-dimensional): definite/indefinite Integral (antiderivative, Riemann sum, main theorem of differential and integral calculus, mean value theorem), integration techniques (substitution, partial integration), integration of power series and rational functions, ideas of numerical integration, improper integrals, various applications.
Module MAT-00-01-M-1
Higher Mathematics I (M, 8.0 LP)
Module Identification
| Module Number | Module Name | CP (Effort) |
|---|---|---|
| MAT-00-01-M-1 | Higher Mathematics I | 8.0 CP (240 h) |
Basedata
| CP, Effort | 8.0 CP = 240 h |
|---|---|
| Position of the semester | 1 Sem. in WiSe/SuSe |
| Level | [1] Bachelor (General) |
| Language | [DE] German |
| Module Manager | |
| Lecturers | |
| Area of study | [MAT-Service] Mathematics for other Departments |
| Reference course of study | [MV-82.103-SG] B.Sc. Mechanical Engineering |
| Livecycle-State | [NORM] Active |
Courses
| Type/SWS | Course Number | Title | Choice in Module-Part | Presence-Time / Self-Study | SL | SL is required for exa. | PL | CP | Sem. | |
|---|---|---|---|---|---|---|---|---|---|---|
| 4V+2U | MAT-00-01-K-1 | Higher Mathematics I
| P | 84 h | 156 h |
U-Schein
| ja | PL1 | 8.0 | WiSe/SuSe |
- About [MAT-00-01-K-1]: Title: "Higher Mathematics I"; Presence-Time: 84 h; Self-Study: 156 h
- About [MAT-00-01-K-1]:
The study achievement "[U-Schein] proof of successful participation in the exercise classes (ungraded)" must be obtained.
- It is a prerequisite for the examination for PL1.
Examination achievement PL1
- Form of examination: written exam (Klausur) (90 Min.)
- Examination Frequency: each semester
- Examination number: 81100 ("Higher Mathematics I")
Evaluation of grades
The grade of the module examination is also the module grade.
Contents
Competencies / intended learning achievements
The following competences are to be promoted:
Professional competence, methodological competence, social competence
Upon successful completion of the module, students will be able
- to deepen the concepts and methods of one-dimensional analysis specific to their subject and their practical application as required in the further course of their studies, since they have acquired a solid basis for the proper handling of mathematics in the engineering sciences;
- to model problems from the engineering sciences and to work on and solve them using mathematical methods, as they have learned and practiced this exemplarily.
In the exercise classes, the students have acquired a confident and independent handling of the terms, statements and methods from the lecture. They can apply the methods and concepts they have learned in examples.
Moreover, In the exercise classes, the presentation and communication skills of the students were trained via the written elaboration of solutions and the presentation in the face-to-face exercise classes. The ability to work in a team was promoted by working in small groups.
Literature
- K. Burg, A. Haf, H. Wille, F. Meister: Höhere Mathematik für Ingenieure,
- G. Bärwolff: Höhere Mathematik für Naturwissenschaftler und Ingenieure,
- T. Rießinger: Mathematik für Ingenieure,
- H. Neunzert, W.G. Eschmann, A. Blickensdörfer-Ehlers, K. Schelkes: Analysis 1.
Registration
Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).